Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - .* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.